Hi good question!
Why is it that many mornings I wake up with an erection (excuse my bluntness)?
I know the scientific reason for this, but if there's a Torah explanation which there probably is, I'm not too sure. If you want the scientific explanation, it might be better that we pm unless the beis din here allows it on public forum.
And like at the same time I have a huge urge to 'letting it stay that way'
You mean once you're aroused in the morning you wanna stay aroused; or do you mean you wanna wake up everyday aroused?
Any suggestions? If there's no real answer as to why it happens and there's nothing really to do about it, any eitzos how to keep myself from touching?
I can't speak for anyone else but practically speaking, it helps to not sleep undressed if I'm trying to avoid arousal. Also, sometimes, going to the bathroom right after I wake up will take care of the problem, but if not, I will distract myself with something like davening, working out, perusing GYE, etc.
Hope this helps!
Benoni